Normal stress differences and beyond-Navier-Stokes hydrodynamics

Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, INDIA

^* e-mail: meheboob@jncasr.ac.in

Published online: 30 June 2017

Abstract

A recently proposed beyond-Navier-Stokes order hydrodynamic theory for dry granular fluids is revisited by focussing on the behaviour of the stress tensor and the scaling of related transport coefficients in the dense limit. For the homogeneous shear flow, it is shown that the eigen-directions of the second-moment tensor and those of the shear tensor become co-axial, thus making the first normal stress difference (N₁) to zero in the same limit. In contrast, the origin of the second normal stress difference (N₂) is tied to the ‘excess’ temperature along the mean-vorticity direction and the imposed shear field, respectively, in the dilute and dense flows. The scaling relations for transport coefficients are suggested based on the present theory.